Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
9751	(2^267149+2562)/2	80420	Stefano Morozzi	01/2020
9752	21321^5908+5908^21321	80411	Hans Havermann	02/2020
9753	(13100^19531-1)/13099	80411	Serge Batalov	08/2020
9754	2^267116-459959	80410	Enzo Doria	06/2015
9755	38715!2+8	80406	Robert Price	01/2015
9756	19579^12786+12786^19579	80406	Hans Havermann	02/2020
9757	(2^267017+1)/3	80380	H.&R. Lifchitz	09/2000
9758	(2^267006+1134)/2	80377	Stefano Morozzi	01/2020
9759	24273^2048+2048^24273	80376	Hans Havermann	01/2020
9760	(2^266989+734)/2	80372	Stefano Morozzi	01/2020
9761	(2^266989+1850)/2	80372	Stefano Morozzi	01/2020
9762	(13427^19471-1)/13426	80372	Serge Batalov	08/2020
9763	2^266968-45	80366	Lelio R Paula	05/2012
9764	(2^266967+3974)/2	80365	Stefano Morozzi	01/2020
9765	20^61768-63	80363	Lelio R Paula	01/2016
9766	(6253^21169-1)/6252	80356	Serge Batalov	08/2020
9767	(14005^19381-1)/14004	80355	Serge Batalov	08/2020
9768	2^266920-112967	80351	Enzo Doria	06/2014
9769	(2^266910+2394)/2	80348	Stefano Morozzi	01/2020
9770	(2^266899+1994)/2	80345	Stefano Morozzi	01/2020
9771	8*10^80342+87	80343	Robert Price	10/2017
9772	(10^80363+1)/11866136004174221950876906463	80335	Anonymous	10/2020
9773	(2^266861+890)/2	80333	Stefano Morozzi	01/2020
9774	12^74428-13	80322	Lelio R Paula	11/2015
9775	(2^266810+2718)/2	80318	Stefano Morozzi	01/2020
9776	(2^266800+2886)/2	80315	Stefano Morozzi	01/2020
9777	(6163^21187-1)/6162	80291	Serge Batalov	08/2020
9778	2^266680+27	80279	Lelio R Paula	05/2012
9779	(232*10^80264+17)/3	80266	Robert Price	04/2021
9780	2^266630-131	80264	Lelio R Paula	05/2012
9781	(2^266627+1278)/2	80263	Stefano Morozzi	01/2020
9782	2^266598+76819	80254	Enzo Doria	05/2016
9783	24463^1908+1908^24463	80253	Hans Havermann	01/2020
9784	2^266587+1880633	80251	Enzo Doria	10/2016
9785	(2^266570+3942)/2	80246	Stefano Morozzi	01/2020
9786	2^266541-110049	80237	Enzo Doria	04/2014
9787	38635!2-8	80222	Robert Price	06/2015
9788	(2^266465+986)/2	80214	Stefano Morozzi	01/2020
9789	3^168111+168111^3-1	80210	Robert Price	04/2014
9790	(2^266447+758)/2	80209	Stefano Morozzi	01/2020
9791	2^266443+513	80208	Lelio R Paula	07/2013
9792	(26*10^80200+61)/3	80201	Robert Price	06/2017
9793	2^266412-109913	80199	Enzo Doria	04/2014
9794	(10223*2^266417+1)/45091	80199	Lelio R Paula	06/2014
9795	2^266413-4693	80199	Yves Minet	05/2019
9796	(13737^19381-1)/13736	80193	Serge Batalov	08/2020
9797	13^71988+66	80191	Lelio R Paula	11/2015
9798	11^77002-4320	80190	Enzo Doria	01/2013
9799	19839^11012+11012^19839	80187	Hans Havermann	03/2020
9801	18^63879-13	80186	Lelio R Paula	11/2015
9800	(2^266371+1814)/2	80186	Stefano Morozzi	01/2020
9802	2^266368-112295	80185	Enzo Doria	06/2014
9803	19217^14880+14880^19217	80185	Hans Havermann	03/2020
9804	(3^168050+5)/1021454	80175	Lelio R Paula	10/2012
9805	(2^266324+1386)/2	80172	Stefano Morozzi	01/2020
9806	(22*10^80167+41)/9	80168	Robert Price	02/2015
9807	(2^266308+1618)/2	80167	Stefano Morozzi	01/2020
9808	(34*10^80162-43)/9	80163	Ray Chandler	12/2010
9809	(2^266276+762)/2	80157	Stefano Morozzi	01/2020
9810	(38*10^80150-11)/9	80151	Robert Price	05/2015
9811	(598*10^80149-31)/9	80151	Robert Price	02/2017
9812	19^62678-80	80150	Lelio R Paula	12/2015
9813	(559^29173-1)/558	80148	Serge Batalov	08/2020
9814	10^80139+32343	80140	Patrick De Geest	02/2011
9815	10^80139-9	80139	Alexander Gramolin	01/2011
9816	3^167955-106	80135	Lelio R Paula	12/2015
9817	20545^7944+7944^20545	80127	Hans Havermann	04/2020
9818	18876^17569+17569^18876	80124	Hans Havermann	03/2020
9819	(2^266137+3782)/2	80115	Stefano Morozzi	01/2020
9820	(2^266121+3846)/2	80111	Stefano Morozzi	01/2020
9821	(22*10^80098+47)/3	80099	Robert Price	06/2021
9822	22752^3313+3313^22752	80093	Hans Havermann	03/2020
9823	(197*10^80089-11)/3	80091	Robert Price	10/2017
9824	2^265998+75559	80074	Enzo Doria	04/2016
9825	(2^265999+3290)/2	80074	Stefano Morozzi	01/2020
9826	2^265969-109801	80065	Enzo Doria	04/2014
9827	(2^265956+3378)/2	80061	Stefano Morozzi	01/2020
9828	(185*10^80051-11)/3	80053	Robert Price	10/2020
9829	2^265888-112757	80041	Enzo Doria	06/2014
9830	(24847^18211-1)/24846	80038	Serge Batalov	08/2020
9831	2^265809+1701	80017	Lelio R Paula	07/2013
9832	gcd(V(957175),5F(191435)(F(191435)+1)+1)	80014	Serge Batalov	04/2015
9833	19807^10954+10954^19807	80012	Hans Havermann	04/2020
9834	3^167687-104	80008	Lelio R Paula	02/2015
9835	11^76826-5790	80007	Enzo Doria	01/2013
9836	10^80000+85731	80001	Patrick De Geest	10/2009
9837	10^80000-7169	80000	Patrick De Geest	09/2009
9838	10^79999+22399	80000	Patrick De Geest	09/2009
9839	10^79999-74873	79999	Patrick De Geest	09/2009
9840	3^167668+58	79998	Lelio R Paula	02/2015
9841	(59*10^79995+391)/9	79996	Robert Price	03/2021
9842	(2^265728+3742)/2	79992	Stefano Morozzi	01/2020
9843	18780^18137+18137^18780	79976	Hans Havermann	04/2020
9844	19190^14709+14709^19190	79976	Hans Havermann	04/2020
9845	155^36506-2	79961	Lelio R Paula	10/2017
9846	(2^265621+3882)/2	79960	Stefano Morozzi	01/2020
9848	2^265612+4257	79958	Lelio R Paula	07/2013
9847	(2^265613+1470)/2	79958	Stefano Morozzi	01/2020
9849	5*3^167577+4	79956	Lelio R Paula	06/2014
9850	(9179*2^265593-1)/9	79955	Lelio R Paula	04/2015
9851	10^79939-7000001	79939	Robert Price	06/2021
9852	6^102723-43	79935	Lelio R Paula	04/2015
9853	21052^6261+6261^21052	79927	Hans Havermann	03/2020
9854	11^76748-3360	79925	Enzo Doria	12/2012
9855	19430^12981+12981^19430	79922	Hans Havermann	03/2020
9856	(2^265490+870)/2	79921	Stefano Morozzi	01/2020
9857	(13*2^265498-1)/187119	79919	Lelio R Paula	02/2014
9858	(2^265438+3978)/2	79905	Stefano Morozzi	01/2020
9859	(2^265409+1250)/2	79896	Stefano Morozzi	01/2020
9860	2^265399-109855	79894	Enzo Doria	04/2014
9861	(2^265380+3930)/2	79888	Stefano Morozzi	01/2020
9862	(20^61403-1)/19	79886	Paul Bourdelais	03/2010
9863	(2^265368+2970)/2	79884	Stefano Morozzi	01/2020
9864	18^63635+59	79880	Lelio R Paula	02/2015
9865	(11*10^79867-107)/3	79868	Robert Price	11/2016
9866	3^167375+80	79859	Lelio R Paula	02/2015
9867	5^114240-14486	79851	Enzo Doria	02/2013
9868	49^47238+48	79842	Norbert Schneider	07/2014
9869	2^265212-3779	79837	Yves Minet	04/2017
9870	(2^265201+2790)/2	79834	Stefano Morozzi	01/2020
9871	91^40746+40746^91	79824	Norbert Schneider	12/2014
9872	(68*10^79813-257)/9	79814	Robert Price	06/2017
9873	(13063^19391-1)/13062	79811	Serge Batalov	08/2020
9874	(5*2^265118-1)/61	79808	Lelio R Paula	02/2014
9875	(2^265102+1462)/2	79804	Stefano Morozzi	01/2020
9876	2^265074+28425	79796	Lelio R Paula	07/2013
9877	2^265072+1185	79795	Lelio R Paula	07/2013
9878	p(16682)#/2-128	79771	Robert Price	05/2017
9879	(2^264994+1714)/2	79771	Stefano Morozzi	01/2020
9881	3^167167-34	79759	Robert Price	11/2013
9880	(2^264952+3258)/2	79759	Stefano Morozzi	01/2020
9882	12^73906+29	79758	Lelio R Paula	02/2015
9883	2^264934+255	79754	Lelio R Paula	07/2013
9884	4*10^79729-87	79730	Robert Price	03/2017
9885	2^264846-111701	79727	Enzo Doria	05/2014
9886	2^264831-112041	79723	Enzo Doria	06/2014
9887	2^264816-455	79718	Yves Minet	03/2012
9888	(55*10^79711+89)/9	79712	Robert Price	09/2017
9889	47^47667-46	79704	Theodore Burton	02/2007
9890	13^71547+96	79700	Lelio R Paula	03/2015
9891	2^264752-112883	79699	Enzo Doria	06/2014
9892	(2^264748+1978)/2	79697	Stefano Morozzi	01/2020
9893	(185*10^79694-11)/3	79696	Robert Price	10/2020
9894	2^264732+133	79693	Lelio R Paula	05/2012
9895	8*3^167010+7	79685	Lelio R Paula	06/2014
9896	42^49087-41	79681	Norbert Schneider	06/2014
9897	(26*10^79678-119)/3	79679	Robert Price	07/2016
9898	2^264683-21	79678	Lelio R Paula	05/2012
9899	7^94279+18	79675	Lelio R Paula	02/2015
9900	2^264655-127	79670	Lelio R Paula	02/2012
9901	(2^264658+3102)/2	79670	Stefano Morozzi	01/2020
9902	(2^264637+1682)/2	79664	Stefano Morozzi	01/2020
9903	2^264597-459043	79652	Enzo Doria	05/2015
9904	(21*2^264566+1)/5	79643	Lelio R Paula	10/2012
9905	2^264536+1870021	79634	Enzo Doria	05/2016
9906	(17*2^264512-1)/359	79625	Lelio R Paula	02/2014
9907	19957^9762+9762^19957	79620	Hans Havermann	03/2020
9908	2^264477-109783	79616	Enzo Doria	04/2014
9909	18^63419-1333	79609	Enzo Doria	03/2013
9910	13^71451-36	79593	Lelio R Paula	03/2015
9911	23314^2593+2593^23314	79590	Hans Havermann	03/2020
9912	3*10^79586+31	79587	Robert Price	06/2021
9913	(2^264410-5)/128002609121	79585	Lelio R Paula	10/2012
9914	19^62234+90	79582	Lelio R Paula	03/2015
9915	(2^264276+2866)/2	79555	Stefano Morozzi	01/2020
9916	12^73714+49	79551	Lelio R Paula	02/2015
9917	(2^264213+1442)/2	79536	Stefano Morozzi	01/2020
9918	(3*2^264184-1)/1433339	79522	Lelio R Paula	02/2014
9919	(2^264160+1590)/2	79520	Stefano Morozzi	01/2020
9920	(29*10^79510-107)/3	79511	Robert Price	08/2020
9921	(9363^20021-1)/9362	79508	Serge Batalov	08/2020
9922	2^264103-112531	79503	Enzo Doria	06/2014
9923	19^62170+78	79501	Lelio R Paula	03/2015
9924	((10^(419875)-1)/9999)18880+1	79501	Matt Stath	01/2021
9925	11^76340-2580	79500	Enzo Doria	12/2012
9926	(2^264084+858)/2	79497	Stefano Morozzi	01/2020
9927	(5652^21187-1)/5651	79495	Serge Batalov	08/2020
9928	(23*10^79492-11)/3	79493	Robert Price	10/2015
9929	((2^132049+13650)^2+(2^132049+13650)+41)/2003/23841473	79491	Makoto Morimoto	05/2016
9930	2^264060-112133	79490	Enzo Doria	06/2014
9931	((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/10426147	79488	Makoto Morimoto	05/2016
9932	20158^8775+8775^20158	79488	Hans Havermann	02/2020
9933	9^83298+6^83298-2^83298	79487	Mike Oakes	08/2010
9934	18^63319+35	79483	Lelio R Paula	02/2015
9935	(10011^19867-1)/10010	79474	Serge Batalov	08/2020
9936	2*10^79468+77	79469	Robert Price	08/2020
9937	22479^3428+3428^22479	79465	Hans Havermann	04/2020
9938	38303!2+256	79461	Robert Price	01/2015
9939	(29*10^79445+61)/9	79446	Robert Price	04/2015
9940	2^263902-195	79443	Lelio R Paula	05/2012
9941	3^166499-112696	79441	Enzo Doria	06/2014
9942	11^76279-2760	79437	Enzo Doria	12/2012
9943	18907^15894+15894^18907	79433	Hans Havermann	03/2020
9944	6^102077-25	79432	Lelio R Paula	03/2015
9945	2^263852-1017	79428	Lelio R Paula	07/2013
9946	2^263842-33	79425	Lelio R Paula	05/2012
9947	(2^263814+3582)/2	79416	Stefano Morozzi	01/2020
9948	12^73584-55	79411	Lelio R Paula	02/2015
9949	(2^263783+3558)/2	79407	Stefano Morozzi	01/2020
9950	2^263772-185	79404	Lelio R Paula	05/2012
9951	(15^67489+1)/16	79373	Paul Bourdelais	03/2010
9952	2^263664+15015	79371	Lelio R Paula	07/2013
9953	(2^263643+1206)/2	79365	Stefano Morozzi	01/2020
9954	(2^263642+3082)/2	79364	Stefano Morozzi	01/2020
9955	(3319^22541-1)/3318	79364	Serge Batalov	08/2020
9956	10^79362+3^79363	79363	Mike Oakes	06/2010
9957	(2^263591+2910)/2	79349	Stefano Morozzi	01/2020
9958	(2^263589+1922)/2	79348	Stefano Morozzi	01/2020
9959	Phi(163244,10)/2448661/6856249	79331	Maksym Voznyy	11/2015
9960	3^166262+44	79328	Lelio R Paula	02/2015
9961	4*10^79327-63	79328	Robert Price	12/2016
9962	2^263486+513	79318	Lelio R Paula	07/2013
9963	(2^263458+1282)/2	79309	Stefano Morozzi	01/2020
9964	(2^263456+1558)/2	79308	Stefano Morozzi	01/2020
9965	2^263448-519509	79306	Paul Bourdelais	03/2013
9966	(18926^18541-1)/18925	79297	Serge Batalov	08/2020
9967	69153^16384+2	79296	Matt Stath	01/2019
9968	21^59971-20^59971	79295	Robert Price	05/2012
9969	2^263372+123	79283	Lelio R Paula	05/2012
9970	(2^263366+1974)/2	79281	Stefano Morozzi	01/2020
9971	17^64429+84	79277	Lelio R Paula	03/2015
9972	11^76124-11430	79275	Enzo Doria	12/2012
9973	19294^12845+12845^19294	79274	Hans Havermann	03/2020
9974	(206*10^79268-17)/9	79270	Robert Price	03/2017
9975	13^71157+18	79265	Lelio R Paula	03/2015
9976	(11*10^79262-23)/3	79263	Robert Price	09/2021
9977	2^263297+65835	79261	Lelio R Paula	07/2013
9978	19^61980-18	79258	Theodore Burton	12/2005
9979	(2^263259+2970)/2	79249	Stefano Morozzi	01/2020
9980	2*10^79242+93	79243	Robert Price	07/2016
9981	(2^263226+1074)/2	79239	Stefano Morozzi	01/2020
9982	(88^40751-1)/87	79238	Paul Bourdelais	08/2017
9983	(103*29^54179-39)/4	79233	Curtis Bright	05/2015
9984	9^83024-83024^9	79226	Norbert Schneider	08/2017
9985	17^64382-26	79219	Lelio R Paula	03/2015
9986	7^93733-74	79214	Lelio R Paula	02/2015
9987	15^67352+38	79213	Lelio R Paula	02/2015
9988	2^263135-110235	79212	Enzo Doria	05/2014
9989	(2^(8768)3^(77475)-1)^(2)-(2^(8768)3^(77475)-1)+41	79209	Tapashree & Jainam	08/2021
9990	(2^263080+3658)/2	79195	Stefano Morozzi	01/2020
9991	2^263044+4257	79185	Lelio R Paula	07/2013
9992	(2^263039+3554)/2	79183	Stefano Morozzi	01/2020
9994	2^263032+87517	79181	Yves Minet	11/2010
9993	6^101755+95	79181	Lelio R Paula	03/2015
9995	(2^263010+1738)/2	79174	Stefano Morozzi	01/2020
9996	4^131497-3^131497	79170	Jean-Louis Charton	05/2004
9997	5*7^93674+8	79165	Lelio R Paula	10/2014
9998	(2^262939+1326)/2	79153	Stefano Morozzi	01/2020
9999	(2^262941+926)/2	79153	Stefano Morozzi	01/2020
10000	lucasU(486,25,29457)-5*lucasU(486,25,29456)	79137	Mike Oakes	05/2009

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Probable Primes Top 10000

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